Three uniforms falling in a set order

Question

Let $A$ , $B$ and $C$ be independent random variables, each uniform on $(0,1)$ . Find the probability that $A\ge B\ge C$ .

Short answer

$1/6$ . Ties have probability zero and the variables are exchangeable, so all $3!=6$ orderings are equally likely and exactly one of them is $A\ge B\ge C$ .

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Counting and Combinatorics
Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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